Biological invasions by large herbivores involve the establishment of novel interactions with the receiving mammalian carnivore community, but understanding these interactions is difficult due to the large spatio-temporal scales at which such dynamics would occur. We quantified the functional responses of a native apex predator (dingo; Canis dingo) and a non-native mesopredator (red fox; Vulpes vulpes) to an invading non-native deer (sambar; Rusa unicolor) in south-eastern Australia. We predicted that the apex predator would exhibit a stronger functional response to increasing sambar abundance than the mesopredator. We used a state–space model to link two 30-year time series: (i) sambar abundance (hunter catch-per-unit-effort), and (ii) percentages of sambar in dingo (N = 4531) and fox (N = 5002) scats. Sambar abundance increased exponentially during 1984−2013. The percentages of sambar in dingo and fox scats increased during this 30-year period, from nil in both species in 1984 to 8.2% in dingoes and 0.5% in foxes in 2013. Dingoes exhibited a much stronger functional response to increasing sambar abundance than foxes. The prediction that invading deer would be utilised more by the apex predator than by the mesopredator was therefore supported. The increasing abundance of sambar during the period 1984−2013 provided an important food source for dingoes. In contrast, the smaller red fox utilized sambar much less. Our study demonstrates that prey enrichment can be an important consequence of large herbivore invasions, and that the effect varies predictably with the trophic position of the mammalian carnivores in the receiving community.